Prior to so-called "frameless" automobiles, there were a number of locations on a vehicle frame that could be engaged for holding part of the frame stationary while a pulling or pushing force was applied to another part of the frame or to the body which was attached to the frame. However, with the advent of "frameless" vehicles, a new mechanism for engaging the vehicle body had to be devised, and this was a clamp which engages a weld seam which usually runs along the lower inner side of the vehicle rocker panel. Normally, such a clamp was secured either to a hold-down on the body shop floor or to a platform upon which the vehicle rested. When using such a clamp, great care must be exercised to distribute the stresses on the undercarriage so as to prevent ripping and twisting of the rocker panels. Another problem had to do with the fact that in some instances the automobile was not raised from the platform, and in others it was jacked up so as to permit access to the underbody and for clearance of measuring systems. Hence, a clamp support capable of being variable in height, depending upon the height of the vehicle with respect to the supporting ramp had to be devised.